Synchronization of biological neural network systems with stochastic perturbations and time delays

With advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in the understanding of the molecular properties of anesthetic agents. However, despite these advances, we still do not understand how anesthetic agents affect the properties of neurons that translate into the induction of general anesthesia at the macroscopic level. There is extensive experimental verification that collections of neurons may function as oscillators and the synchronization of oscillators may play a key role in the transmission of information within the central nervous system. This may be particularly relevant to understand the mechanism of action for general anesthesia. In this paper, we develop a stochastic synaptic drive firing rate model for an excitatory and inhibitory cortical neuronal network in the face of system time delays and stochastic input disturbances. In addition, we provide sufficient conditions for global asymptotic and exponential mean-square synchronization for this model.